Jelly, (削除) 32 (削除ここまで) 27 bytes
,U=€JẸ,E,SÆ2$
ZL«L’aL€Ç$æA/
Now taking input at a list of lines and switched &g×ばつ with ’a and using SÆ2 after L€ instead of FLÆ2Ɗ. These allowed me to condense into two lines and I saved 5 bytes in total. The following values are the same as before.
[0.0, 0.0]=Mess
[0.0, 1.5707963267948966]=Rectangle
[0.0, 0.7853981633974483]=Square
[1.5707963267948966, 0.0]=Triangle
ZL«L gets the minimum of height and width and ’ subtracts 1 from it. Ç calls the second link and at the end if the input is a single line the result of Ç gets logical ANDed with the previous number if there is only a single line the output will be [0.0, 0.0].
In the second link: ,U yields a list of line lengths paired with it's reverse. J is range(number of lines) and =€ checks whether each of them are equal to the result of J. Ẹ (Any) yields 1 if the input is a triangle.
E checks if all line lengths are equal (rectangle/square).
SÆ2 with a $ to group them into a single monad checks whether the total number of characters is a square number.
So at the end of the second link we have [[a,b],c] where each number is 0 or 1 indicating whether the input is a triangle, rectangular, and has square number of characters respectively.
However a square number of elements doesn't imply the input is a square since an messy input like
a3.
4
has a square number of elements but isn't a square.
This is where æA (arctan2) comes in. 0æA0 == 0æA1 == 0. In other words, if the input has square number of elements but is not a rectangle, then it is not a square. There are certainly more clear ways to do this but what does that matter when we have bytes to think about and we are allowed consistent arbitrary output.
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